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How Do Read-Once Formulae Shrink?

Published online by Cambridge University Press:  12 September 2008

Moshe Dubiner  and
Uri Zwick
Moshe Dubiner
Affiliation:
The School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv university, Tel Aviv 69978, Israel e-mail: [email protected]
Uri Zwick
Affiliation:
The School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv university, Tel Aviv 69978, Israel e-mail: [email protected]
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Abstract

Let f be a de Morgan read-once function of n variables. Let fε be the random restriction obtained by independently assigning to each variable of f, the value 0 with probability (1 -ε)/2, the value 1 with the same probability, and leaving it unassigned with probability ε. We show that fε depends, on the average, on only O(εαn + εn1/α) variables, where . This result is asymptotically the tightest possible. It improves a similar result obtained recently by Håstad, Razborov and Yao.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 4 , December 1994 , pp. 455 - 469
Copyright
Copyright © Cambridge University Press 1994

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